Straw faced criticism during the weekend for allegedly covering up the details of conversations he had with a lobbyist for supermajor BP over Libyan oil deals reached before the release of Lockerbie bomber Abdel Basset al-Magrahi.
Scottish Justice Minister Kenny MacAskill on Aug. 20 released Magrahi, the lone suspect in the 1988 bombing of Pan Am Flight 103, on compassionate terms as the former Libyan intelligence officer suffers from terminal cancer.
Allegations have surfaced that a 2007 bilateral prisoner transfer agreement between the British government and Tripoli was linked to oil contracts and the Magrahi release.
Straw said he spoke with former British intelligence officer and BP consultant Mark Allen in 2007 but stressed that "at no stage" were the talks linked to the Magrahi release and oil contracts, London's Independent newspaper reports.
Straw, however, turned down an FOI request that sought details on the talks he held with Allen, the report said.
BP in 2007 inked a $900 million exploration deal with Libya but worried talks over a prisoner transfer agreement with Libya would undermine the contract.